I want the Super key to behave as a regular modifier key, just like Ctrl, Shift and Alt.

Currently, it doesn't.

Using the System Settings to set a shortcut like Super+Up will set the shortcut, but the shortcut will be unusable. Pressing Super+Up instead functions just like pressing a single Up. The Super modifier is ignored and the shortcut never gets actived. Likewise for shortcuts such as Super+W (i.e. it's like pressing an unmodified single W).

I've used CompizConfig to unbind all Unity-related shortcuts, but Super still behaves in this weird, special way.